ECAT Pre General Science MCQ Test With Answer for Mathematics Chapter 9

Two unbiased dice are thrown. The probability that the total score is > 5 is

• 1 / 18 A
• 7 / 18 B
• 13 / 18 C
• 11 / 18 D

Three integers are chosen at random from the first 20 integers. Then probability that their product is even, is

• 2 / 19 A
• 3 / 29 B
• 17 / 19 C
• 4 / 19 D

• 
  A
• 
  B
• 
  C
• 
  D

The number of words that can be formed out of the letters of the word ASSASSINATION is

• 
  A
• 
  B
• 
  C
• 
  D

• 110 A
• 220 B
• 1320 C
• None of these D

If A is an event then which of the following is true

• P(A)<0 A
• 0≥P(A)≤1 B
• P(A)>0 C
• None D

• 
  A
• 
  B
• 
  C
• 
  D

Product of any n consecutive positive integers is divisible by

• n A
• √n B
• n! C
• None D

A die is rolled. What is the probability that the dots on the top are greater than 4?

• 1/4 A
• 1/2 B
• 1/3 C
• 1/33 D

Out of 40 consecutive natural numbers, two are chosen at random. Probability that the sum of the numbers is odd, is

• 14 / 29 A
• 20 / 39 B
• 1 / 2 C
• n D

• 36 A
• 360 B
• 24 C
• 6 D

A key ring is an example of

• Permutation A
• Circular permutation B
• Combination C
• None D

A and B throw a dice. The probability that A's throw is not greater then B's is

• 5 / 12 A
• 7 / 12 B
• 1 / 6 C
• 1 / 2 D

The value of n, when ⁿP₂= 20 is

• 3 A
• 4 B
• 6 C
• 5 D

A combination lock on a suitcase has 3 wheels each labeled with nine digits from 1 to 9. If an opening combination is a particular sequence of three digits with no repeats, the probability of a person guessing the right combination is

• 1 / 500 A
• 1 / 504 B
• 1 / 252 C
• 1 / 250 D

A die is thrown 100 times. If getting an odd number is considered a success, the variance of the number of successes is

• 50 A
• 25 B
• 10 C
• 100 D

• n! A
• 0! B
• 1 C
• None of these D

How many 6-Digit number can be formed without repairing any digit from the digits 0,1,2,3,4,5

• 720 A
• 600 B
• 120 C
• 6-5! D

Fifteen girls compete in a race. The first three places can be taken by them in

• 3! ways A
• 12! ways B
• 15 x 14 x 13 ways C
• 42 ways D

How many arrangements of the letter of the word PAKPATTAN can be made

• 
  A
• 
  B
• 
  C
• 
  D

• 0.9 A
• 0.74 B
• 0.2016 C
• None of these D

The domain of a finite sequence is a

• Set of natural numbers A
• R B
• Subset of N C
• Proper subset of N D

The key for opening a door is in a bunch of 10 keys. A man attempts to open the door by trying the keys at random discarding the wrong key. The probability that the door is opened in the 5th trial is

• 1 / 10 A
• 2 / 10 B
• 3 / 10 C
• 4 / 10 D

• 
  A
• 
  B
• 
  C
• 
  D

There are n seats round a table numbered 1, 2, 3 .... n. The number of ways in which m person can take seats is

• ⁿP_m A
• ⁿC_mx (m - 1) ! B
• ^n-1P_m C
• None of these D

If A and B are two disjoint events then

• P(A∪B)=P(A)+P(B) A
• P(A∪B)=P(A)-P(A∪B) B
• P(A∪B)=P(A)or P(B) C
• None D

A machine operates if all of its three components function. The probability that the first component fails during the year is 0.14, the second component fails is 0.10 and the third component fails is 0.05. the probability that the machine will fail during the year is

• 0.2647 A
• 0.2692 B
• 0.3647 C
• None of these D

n(n - 1) (n - 2) in factorial form is

• 
  A
• 
  B
• 
  C
• 
  D

The number of significant numbers which can be formed by using any number of the digits 0, 1, 2, 3, 4 but using each not more than once in each number is

• 260 A
• 356 B
• 410 C
• 96 D

• 3 A
• 6 B
• 0 C
• None of these D